Controlled ripple texturing and Raman spectroscopy in suspending graphene

林永昌20, Aug. 2010

Wrinkling of skin

E. Cerda and L. Mahadevan, PRL 90, 074302(2003)

polyethyleneL=25cm, W=10cm, t=0.01cmUniaxial tensile strain ϒ=0.1.

A drying apple

The wrinkles are orthogonal to the boundary

Compression wrinkles

Human skin

Out-of-plane displacement of the ripples

Wenzhong Bao et al., Nature nanotech 4, 562 (2009).

Wrinkling of graphene

Wenzhong Bao et al., Nature nanotech 4, 562 (2009).

ϒ: longitudinal tensile strain

ν: the Poisson ratio€

ν =−dε transdεaxial

transverse strain (negative for axial tension (stretching), positive for axial compression)

Single-layer graphene ν ≈ 0.1-0.3 (graphite = 0.165)

axial strain (positive for axial tension, negative for axial compression)

A: amplitude, λ: wavelength

(1)

(2)

TrenchDepth=100~250nmWidth=2~4um

Exfoliated graphene(shear)

Thin-film elasticity theory

(The applied stress is dominated by in-plane shear)

(1), (2) Thicker film: ~0.016-0.3%Thinner film: up to 1.5%

Wenzhong Bao et al., Nature nanotech 4, 562 (2009).

Controllably produce ripples by thermal manipulation

• Process:– Heating the sample up to 700K then cool down slowly.– Ripples appear during the cooling down to 300K.

• During thermal cycling, the graphene membranes experience a competition between three forces: – Fpin: the substrate-pinning force that prevents the graphene

membrane from sliding.– Fb: the bending/buckling critical compression force, which is generally

much less than Fpin.

– Fstretch: the elastic restoring force under tension.

Wenzhong Bao et al., Nature nanotech 4, 562 (2009).

Fpin Fb

FstretchFstretch

Biaxial compression

When T increase,Substrate and trench width expand biaxially while graphene contracts. Fstretch > Fpin:The taut membrane slides over the substrate into the trench, hence erasing any pre-existing ripples.

Cooling process applies compressive stress, Fb << Fpin:The ends of the graphene remain pinned to the banks of the trench, resulting in transverse (y) ripples and longitudinal (x) buckling.

Wenzhong Bao et al., Nature nanotech 4, 562 (2009).

y

x

Thermal expansion coefficient (α) of suspended graphene

Graphene ‘s TEC α(T) is calculated from slope of the curve

700K -> 450K -> 300KA sagging graphene

Graphene α ≈ -7x10-6 K-1 at 300K.

Wenzhong Bao et al., Nature nanotech 4, 562 (2009).

αSi≈3x10-6 K-1

αSiO2≈5x10-6 K-1

αNi≈13x10-6 K-1

αCu≈17x10-6 K-1

€

∂ωG

∂ε= −58cm−1%

€

∂ωG

∂ε= −30cm−1%

€

∂ωG

∂ε= −58cm−1%

Uniaxial strain

biaxial strain

Strain-induced downshifts of the G band(first principals calculations)

Biaxial compression induced Raman G shift

Upshift 25cm-1

Effective contraction of graphene

≈0.40% Average amplitude A=5.2nmWavelength λ=0.26μm

Chun-Chung Chen et al., Nanolett 9, 4172 (2009).

(Taylor expansion)

Estimated compression from Raman G shift

Tensile strain

Compress strain

Chun-Chung Chen et al., Nanolett 9, 4172 (2009).

Raman G peak and linewidth shifts

Chun-Chung Chen et al., Nanolett 9, 4172 (2009).

Electric transport properties

Wenzhong Bao et al., Nature nanotech 4, 562 (2009).

higher mobility

Smaller density of charged impuritiesContaining ripple on suspended graphene

Summary

• Control and manipulate the ripples in graphene sheets represents the first step towards strain-based graphene engineering.

• Large and negative thermal expansion coefficient of graphene ≈ -7x10-6 K-1 at 300K

• Significant upshift of Raman G peak (25cm-1) corresponds to compressions in the substrate region up to 0.4%.

reference

• Wenzhong Bao et al., Nature nanotech 4, 562 (2009).

• Chun-Chung Chen et al., Nanolett 9, 4172 (2009).

• E. Cerda and L. Mahadevan, PRL 90, 074302(2003).